Under assumption REF , the classical extreme value theorem of [1]} applies to the latent noiseless distribution \(F\) ; see theorem REF  below.See chapters 1-2 in [2]} and chapters 1-5 in [3]} for a thorough treatment of extreme value theory for iid observations. This will serve as the basis for extending this extreme value convergence to the observed noisy data. Without assumption REF , we would not be able to conduct inference using the asymptotic behavior of the sample maximum even if we had access to the true \(\theta _i\) . Assumption
REF  is a fairly mild assumption, satisfied by almost all textbook continuous distributions and many discrete ones.
